# Angular dependence of electron-positron to two photons

• wasia
In summary, the dominating process for electron-positron annihilation at low energies is photon pair creation, and the angular dependence of the total cross section is spherically symmetric in the center of mass system. The invariant matrix element does not depend on the angle due to the electron and positron annihilating from a state of zero total spin and zero angular momentum. However, for exactly two photons, the distribution is isotropic, while for three photons it becomes more complex.
wasia
Hello,

First of all, it is not a homework question, just something I wonder about.

The dominating electron-positron annihilation process at low energies is photon pair creation. What is the angular dependence of the total cross section?

For some reason I expect the head-on collision to have the highest cross-section and the collinear situation to have the lowest cross-section, is it really the case?

I am not a particle physicist, but I expect the calculation to be pretty difficult, involving IR divergences and collinear divergences. Could you give me a reference to the solution of the problem or the experimental results and perhaps give some physical intuition on the whole thing.

"I expect the head-on collision to have the highest cross-section and the collinear situation to have the lowest cross-section"
I don't know what you mean by this.
In the center of mass system, it is always head-on.
In that system, the photon distribution is spherically symmetric.
The distribution in other initial configurations can be found by Lorentz transformation.

Do I understand correctly that you claim that the invariant matrix element does not depend on the angle?

Yes. The electron and positron annihilate from a state of zero total spin and zero angular momentum so there is no angular distributon of the two photons.

But that's only half the answer. Why zero total spin?

That's more subtle - the answer there is that state has to produce three photons. So for exactly two photons, it's isotropic.

## 1. What is the "Angular Dependence" in the context of electron-positron to two photons?

The angular dependence refers to the relationship between the direction of propagation of the electron-positron pair and the direction of emission of the two photons produced from their annihilation. This angular dependence can be described using mathematical equations and is an important factor in understanding the behavior of electron-positron pairs and their resulting photon emissions.

## 2. How is the angular dependence of electron-positron to two photons measured?

The angular dependence can be measured experimentally using detectors that can detect the direction of the emitted photons. By analyzing the distribution of these photons in different directions, scientists can determine the angular dependence of the electron-positron pair to two photons.

## 3. What factors influence the angular dependence of electron-positron to two photons?

The angular dependence is influenced by the spin of the electron and positron, their relative velocities, and the direction of their initial motion. Additionally, the presence of external fields, such as magnetic fields, can also affect the angular dependence.

## 4. Why is the study of the angular dependence of electron-positron to two photons important?

Understanding the angular dependence is crucial in many areas of physics, such as particle physics and astrophysics. It can provide insights into the fundamental properties of particles and their interactions, as well as help in the development of new technologies, such as advanced detectors and accelerators.

## 5. Can the angular dependence of electron-positron to two photons be predicted?

Yes, the angular dependence can be predicted using theoretical models and calculations. However, experimental results are needed to confirm these predictions and further refine our understanding of this phenomenon.

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